Exercise 75 Page 394

Practice makes perfect

a When rewriting a radical into exponential form, the exponent of the radicand is the numerator of the rational exponent, and the index of the radical is the denominator of the rational exponent.

sqrt(a)=a^()1 n and sqrt(a^m)=a^() m n With this in mind, we can rewrite the given expression. &(sqrt(3x))^3 ⇔ ((3x)^()1 2 )^3 Now, let's simplify this expression as much as possible.

((3x)^()12 )^3

PowPow

(a^m)^n=a^(m* n)

(3x)^(12 * 3)

MoveRightFacToNumOne

1/b* a = a/b

(3x)^()32

b When rewriting a radical into exponential form, the exponent of the radicand is the numerator of the rational exponent, and the index of the radical is the denominator of the rational exponent.

sqrt(a)=a^()1 n and sqrt(a^m)=a^() m n With this in mind, we can rewrite the given expression. &sqrt(81) ⇔ 81^()1 x

c When rewriting a radical into exponential form, the exponent of the radicand is the numerator of the rational exponent, and the index of the radical is the denominator of the rational exponent.

sqrt(a)=a^()1 n and sqrt(a^m)=a^() m n With this in mind, we can rewrite the given expression. &(sqrt(17))^x ⇔ (17^()1 3 )^x Now, let's simplify this expression as much as possible.

(17^()13 )^x

PowPow

(a^m)^n=a^(m* n)

17^(13 * x)

MoveRightFacToNumOne

1/b* a = a/b

17^()x3